Scholarlink

<p>The study of interpolation nodes and their associated Lebesgue constants is central to numerical analysis, impacting the stability and accuracy of polynomial approximations. In this paper, we will explore the Morrow–Patterson points, a set of interpolation nodes introduced to construct cubature formulas of a minimum number of points in the square for a fixed degree <i>n</i>. We prove that their Lebesgue constant growth is <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\mathcal {O}}(n^2)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">O</mi> <mo stretchy="false">(</mo> <msup> <mi>n</mi> <mn>2</mn> </msup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> as was conjectured based on numerical evidence about 20&#xa0;years ago in the paper by Caliari et al. (Appl Math Comput 165(2):261–274, 2005).</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On the Lebesgue Constant of the Morrow–Patterson Points

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年5月14日

查看全文
  • Tomasz Beberok,
  • Leokadia Bialas-Ciez,
  • Stefano De Marchi

摘要

The study of interpolation nodes and their associated Lebesgue constants is central to numerical analysis, impacting the stability and accuracy of polynomial approximations. In this paper, we will explore the Morrow–Patterson points, a set of interpolation nodes introduced to construct cubature formulas of a minimum number of points in the square for a fixed degree n. We prove that their Lebesgue constant growth is \({\mathcal {O}}(n^2)\) O ( n 2 ) as was conjectured based on numerical evidence about 20 years ago in the paper by Caliari et al. (Appl Math Comput 165(2):261–274, 2005).